TY - JOUR
T1 - A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem
AU - Delaigle, Aurore
AU - Fan, Jianqing
AU - Carroll, Raymond J.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Carroll's research was supported by grants from the National Cancer Institute (CA57030, CA90301) and by award number KUS-CI-016-04 made by the King Abdullah University of Science and Technology (KAUST). Delaigle's research was supported by a Maurice Belz Fellowship from the University of Melbourne, Australia, and by a grant from the Australian Research Council. Fan's research was supported by grants from the National Institute of General Medicine R01-GM072611 and National Science Foundation DMS-0714554 and DMS-0751568. The authors thank the editor, the associate editor, and referees for their valuable comments.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2009/3
Y1 - 2009/3
N2 - Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last 15 years. We propose an innovative local polynomial estimator of any order in the errors-in-variables context, derive its design-adaptive asymptotic properties and study its finite sample performance on simulated examples. We provide not only a solution to a long-standing open problem, but also provide methodological contributions to error-invariable regression, including local polynomial estimation of derivative functions.
AB - Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last 15 years. We propose an innovative local polynomial estimator of any order in the errors-in-variables context, derive its design-adaptive asymptotic properties and study its finite sample performance on simulated examples. We provide not only a solution to a long-standing open problem, but also provide methodological contributions to error-invariable regression, including local polynomial estimation of derivative functions.
UR - http://hdl.handle.net/10754/597252
UR - http://www.tandfonline.com/doi/abs/10.1198/jasa.2009.0114
UR - http://www.scopus.com/inward/record.url?scp=70349761934&partnerID=8YFLogxK
U2 - 10.1198/jasa.2009.0114
DO - 10.1198/jasa.2009.0114
M3 - Article
C2 - 20351800
SN - 0162-1459
VL - 104
SP - 348
EP - 359
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 485
ER -